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48 MOLECULAR MOTION AND ITS ENERGY 25 



the energy of the molecular motion, but also that of the 

 motions of the individual atoms, which presumably consist 

 of oscillations and rotations about the common centroid. 



The proposition of the conservation of energy makes it 

 necessary to admit certain assumptions, which, indeed, 

 would be contested by no one, but which are only hypotheses, 

 since they fail to possess the certainty afforded by a mathe- 

 matical proof. In the particular case when we apply this 

 proposition to a system of material particles endowed with 

 mutual attraction or repulsion, the most essential of these 

 hypotheses is that the action of one particle on another is 

 equal to the reaction exerted on the first by the second. 



If this assumption is admitted, no further hypothesis is 

 needed for the proof of Maxwell's law save the proposition 

 y of the conservation of energy, the other general theorems of 

 / analytical mechanics which are used for the mathematical 

 proof being immediate consequences of this assumption 

 regarding action and reaction. This applies especially to the 

 theorem of the Conservation of Momentum of the centroid 

 of a system a theorem which is brought into our proof 

 only when the gas possesses a general forward velocity in 

 addition to its internal heat-motion, i.e. when it is in a 

 state of flow. The same is true with regard to the so- 

 ailed theorem of the Conservation of Areas or of the 

 Moments of Momenta', this comes into consideration only 

 when the gas is in a state of rotation. 



If then no further hypotheses are needed for the proof 

 of Maxwell's law, the assumption underlying the first 

 proofs, viz. that the molecules are simple material points, 

 can especially be dispensed with. The law therefore holds 

 not only for monatomic molecules, i.e. such as consist of a 

 single atom or one massive point, but also for polyatomic 

 molecules or chemical combinations of several atoms. 



That this extension of M a x w e 11 ' s law to compound mole- 

 cules is admissible was first recognised by Boltzmann 1 

 who has thereby exercised a very important influence on the 

 further development of the theory. 



It must, however, not be overlooked that the law has 



1 Wiener Sitzungsber. Ixiii. 2. Abth. 1871, p. 397. 



